The phenomenon of noise enhanced signal transfer, or stochastic
resonance, has been observed in many nonlinear systems such as
neurons and ion channels. Initial studies of stochastic resonance
focused on systems driven by a periodic signal, and hence used a
signal to noise ratio based measure for comparison between the
input and output of the system. It has been pointed out that for
the more general case of aperiodic signals other measures are
required, such as cross-correlation or information theoretical
tools. In this paper we present simulation results obtained in a
model neural system driven by a broadband aperiodic signal, and
producing a signal imitating neural spikes. The system is analyzed
by using cross-spectral measures.
Finite pulse width effects in level crossing detectors and similar systems, such as neurons, cause an output noise which is a monotonically increasing function of frequency in the low frequency limit. The effect is also relevant for shot noise phenomena with reduced strength.
Shannon's information rate formula does not work for wideband (aperiodic) signals with nonlinear transfer. The classical signal and noise measures used to characterize stochastic resonance do not work either because their way of distinguishing signal from noise fails. In a study published earlier, a new way of measuring and identifying noise and aperiodic (wideband) signals during strongly nonlinear transfer was introduced. The method was based on using cross-spectra between the input and the output. According to the study, in the case of linear transfer and sinusoidal signals, the method gives the same results as the classical method and in the case of aperiodic signals it gives a sensible measure. In this paper we refine the theory and present detailed simulations which validate and refine the conclusions reached in that study. The simulation results clearly confirm that the cross-spctral identifications of output signal and noise are sensible measures and we put the theory on a firm footing. As neural and ion channel signal transfer is nolinear and aperiodic, the new method has direct applicability in biophysics and neural science.